The leader of the opposition said he was even more appalled that the newspaper refused to apologise over a controversial article that said the beliefs of Ralph Miliband "should disturb everyone who loves this country".

"I'm furious because what is political debate coming to in this country when this happens? That's why I've spoken out," he said in a television interview with BBC News on Tuesday. "It's an unusual step to speak out. I don't do it lightly but I am not willing to see my father's good name undermined in this way."

"I was appalled when I read the Daily Mail on Saturday and saw them saying that he hated Britain. It's a lie," the visibly angry Labour leader told the BBC.

"I'm even more appalled that they repeated that lie today and have gone further and described my father's legacy as 'evil'. Evil is a word reserved for particular cases and I was not willing to let that stand.

"It's perfectly legitimate for the Daily Mail to talk about my father's politics but when they say that he hated Britain I was not willing to put up with that because my father loved Britain, my father served in the Royal Navy, he was a refugee who came here and found security in this country.

"What I'm interested in is defending my father's good name. I don't want the British people to think my father hated Britain – because he loved Britain. When the Daily Mail not only says that but publishes a photo on its website of his gravestone with a pun about it saying he was a grave socialist … I'm furious because what is political debate coming to in this country when this happens? That's why I've spoken out."

He added that the row was not about regulating the press or a desire to stifle what newspapers write about his father, a prominent socialist scholar. "There are boundaries. Newspapers and people across politics must not overstep those boundaries," he said. "It's not about government or politics stepping in and stopping that happening it's about the way we conduct our debates in this country."

Miliband said he had spoken to his brother David, the former Labour MP, and his mother about the Daily Mail article. "It feels so jarring with what we know about my dad. I know my dad better than anybody, as do David and my mum, and when we used to go on holiday what was the thing he used to look forward to doing most? It was coming back to Britain because he loved this country so much," he said.

"Britain saved his life and this paper is saying that he hated Britain and that is a lie. It is a lie and I'm not willing to let it stand."

The row showed no sign of defusing when, shortly after Miliband's television interview, a spokesman for the Daily Mail maintained that the newspaper was right to tell its readers that the Labour leader's father "hated British institutions".

The spokesman said: "We ask fair-minded people to read our editorial today. For what this episode confirms is that you cannot allow politicians anywhere near regulating the press.

"While we respect Mr Miliband's right to defend his father – and he has done so in the Daily Mail today – it is worth stressing that Ralph Miliband wasn't an ordinary private individual but a prominent academic and author who devoted his life to promoting a Marxist dogma which caused so much misery in the world. He hated such British institutions as the Queen, the church and the army, and wanted a workers' revolution. Our readers have a right to know that."

The spokesman described Ed Miliband as a leading advocate of statutory regulation of the press and said his father was "a proponent of one of the world's most poisonous political doctrines under which freedom of expression was crushed and newspapers controlled by governments".

David Cameron and Nick Clegg waded into the row on Tuesday, backing Miliband's response. Cameron said he had not read the original article but said that "if anyone had a go at my father, I would want to respond vigorously".

Clegg wrote on Twitter: "I support Ed Miliband defending his dad. Politics should be about playing the ball, not the man, certainly not the man's family."

David Miliband tweeted: "My dad loved Britain. Here's the truth," and linked to his brother's article defending their father, who fled Belgium aged 16 to escape the Nazis.

Ed Miliband wrote in the Mail: "There is no credible argument in the article or evidence from his life which can remotely justify the lurid headline and its accompanying claim that it would 'disturb everyone who loves this country'."

Critics of the Mail highlighted the paper's stance on Oswald Mosley's British Union of Fascists in the 1930s. Lord Prescott, the former deputy prime minister, posted a picture of a Daily Mail article by Viscount Rothermere published eight decades ago headlined: Hurrah for the Blackshirts, and said: "Here's a Daily Mail leader praising fascists written by the great-grandfather of the paper's current owner."

The Bradford West MP George Galloway said: "How low can the Daily Mail sink? How about its despicable smear on Jewish refugee from Nazism and D-Day vet Ralph Miliband? The Daily Mail which supported fascism and ran a front page splash in support of British Nazis titled 'Hurrah for the Blackshirts!'"

Raymond Snoddy, the prominent media commentator, said the Mail owed Miliband an apology for its latest attack. "Daily Mail really hasn't sustained the case that Miliband snr was The Man Who Hated Britain merely Marxist class warrior. An apology is due," he tweeted.

Owen Jones, the Independent columnist and socialist commentator, said: "Weirdly compelling how all the worst elements of our country – fear, prejudice, hate – have been stuffed into paper form, aka the Daily Mail."

The Labour MP Paul Farrelly said the Mail's "disgraceful smear" was linked to Ed Miliband's backing of an independent press watchdog that would limit the involvement of newspaper owners.

"The Daily Mail continues to plumb new depths in its attacks on both Labour and Ed Miliband, he said. "People should be under no illusion that this campaign of intimidation is not just political, but highly personal – because Ed has come out strongly for a truly independent press watchdog, not controlled by the likes of Mail editor Paul Dacre.

"This disgraceful smear of Ed's dead father shows once again what a mockery it is for the Mail's editor to have overseen the code on standards at the discredited Press Complaints Commission. The sooner our media moves on from this sort of behaviour, the better."

The Guardian has published an extensive critique of the Daily Mail and its reporting of Labour, press regulation and the Snowden leaks. We invited Mail readers to join in that debate. Paul Dacre, editor-in-chief, asked for the opportunity to comment. Here is his contribution